Question: Solve for $x$ : $6x^2 - 72x + 162 = 0$
Dividing both sides by $6$ gives: $ x^2 {-12}x + {27} = 0 $ The coefficient on the $x$ term is $-12$ and the constant term is $27$ , so we need to find two numbers that add up to $-12$ and multiply to $27$ The two numbers $-9$ and $-3$ satisfy both conditions: $ {-9} + {-3} = {-12} $ $ {-9} \times {-3} = {27} $ $(x {-9}) (x {-3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -9) (x -3) = 0$ $x - 9 = 0$ or $x - 3 = 0$ Thus, $x = 9$ and $x = 3$ are the solutions.